Interpretive Summary: Many earthen dams that were originally built to protect agricultural land from flooding are now protecting residential and commercial property. These changes have taken place over a period of 50 years or more, and as a result, these dams need evaluation to assure they are designed according to current dam safety regulations. In some instances, the spillway capacity of these dams is inadequate to carry the design flood flow downstream. To address this issue, roller compacted concrete (RCC) stepped spillways have become a popular choice for dam overtopping protection. Researchers at the USDA-ARS Hydraulic Engineering Research Unit in Stillwater are conducting studies to evaluate the design of stepped spillways. Equations are being developed to determine the design properties of the spillway (i.e. wall height) and for sizing the stilling basin. The focus of this paper is to introduce new equations for determining the flow depth in stepped spillways.

Technical Abstract:
A common deficiency for embankment dams changing from a low hazard to a high hazard dam is inadequate spillway capacity. Roller compacted concrete (RCC) stepped spillways are a popular method to address this issue. Stepped spillway research has gained momentum in recent years due to the need for design guidance when an RCC spillway is retrofitted to an existing embankment. Researchers at the USDA-ARS Hydraulic Engineering Research Unit (HERU) in Stillwater, OK, are conducting generalized research on RCC stepped spillways to provide the design guidance necessary to determine stepped spillway design parameters including inception point, flow depth, air entrainment, and energy dissipation. The research has shown the normalized clear water flow depth downstream of the inception point is a function of chute slope and the ratio of step height to critical depth, and the normalized flow depth upstream of the inception point is a function of chute slope, the ratio of step height to critical depth, and the normalized length from the crest. The objective of this paper is to introduce two new relationships that can be used to determine the flow depth at any location upstream and downstream of the inception point for stepped spillways on embankment dams.